Topology Seminar

Date: November 10, 2021

Time: 4:00PM - 4:50PM

Location: zoom

Speaker: Dylan Wilson, Harvard University

Title: Higher Bott periodicities in Algebraic K-theory

Abstract: Algebraic K-theory is a powerful invariant that encodes a lot of information in number theory and geometric topology. One of the deepest theorems about the algebraic K-theory of number rings is that it approximately behaves like complex topological K-theory, which famously satisfies Bott periodicity (this is the Lichtenbaum-Quillen conjecture, now resolved by work of Voevodsky and many others). I will describe joint work with Jeremy Hahn where we exhibit an analog of this result involving periodicities of larger and larger 'wavelength', thus affirming the Redshift Conjecture of Ausoni-Rognes for a large class of examples.